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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.07855 |
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Table of Contents:
- For the Hill equation describing one-dimensional periodic systems, a constructive formulation is developed for generating Floquet-Bloch states directly from arbitrary pairs of linearly independent solutions. One-dimensional photonic crystals are used as a concrete illustration. Explicit closed-form formulas map an arbitrary fundamental system to the corresponding Floquet-Bloch basis via the monodromy matrix, including the generic Jordan band-edge case, without reliance on canonically normalized solutions. The construction can be expressed directly in terms of the transfer matrix, making the residual representation freedom transparent and providing an implementation-ready framework for analytical and numerical studies of periodic systems.